I am trying to get the Character Viewer to show up in the menu for inputing special mathematical characters into text.

I set the checkbox and go back outside to system preferences main screen and when I return the checkbox is unchecked. No matter how I leave the screen after checking the checkbox it will disappear upon my return.

I brought my machine to my local Apple Store and troubleshooted the issue with a Genius.

We we're removing plist files in my Library and seeing if the issue resolved it itself when the plist files were regenerated by OS X. Nothing worked so far.

We could see that every time we checked the checkbox two plist files would be created momentarily and then deleted immediately after.

Finally we stumbled upon com.apple.CharacterPaletteIM.plist. We removed it and re-checked the checkbox and bam issue solved. The funny thing is that file has nothing to do with the Special Character Viewer. I then noticed that doing this also added an icon in the top right menu bar which indicates the current language of the keyboard.

Then it clicked in my head that I had set a setting during the initial setup of my machine to hide this icon in the top menu bar. I went back to System Preferences -> Keyboard -> Input Sources and looked at the following setting:

Low and behold the setting was checked on even though I had checked it off 5 days ago. I went back to System Preferences -> Keyboard -> Keyboard and toggled the checkbox for the Character Viewer on and off several times and it worked.

I went back to the Input Source tab and toggled the keyboard language menu bar setting off. I returned to the Keyboard tab and the checkmark had been removed from the checkbox already! Toggling it on and off had no effect. I had reproduced the issue and I could repeat it every time without fail.

TL;DR
There is a bug in Mavericks that will not let you have the Special Character Viewer if you don't have your Keyboard Input Menu icon visible in the menu bar. See pictures above.​

I brought my machine to my local Apple Store and troubleshooted the issue with a Genius.

We we're removing plist files in my Library and seeing if the issue resolved it itself when the plist files were regenerated by OS X. Nothing worked so far.

We could see that every time we checked the checkbox two plist files would be created momentarily and then deleted immediately after.

Finally we stumbled upon com.apple.CharacterPaletteIM.plist. We removed it and re-checked the checkbox and bam issue solved. The funny thing is that file has nothing to do with the Special Character Viewer. I then noticed that doing this also added an icon in the top right menu bar which indicates the current language of the keyboard.
.....

Low and behold the setting was checked on even though I had checked it off 5 days ago. I went back to System Preferences -> Keyboard -> Keyboard and toggled the checkbox for the Character Viewer on and off several times and it worked.
.....

TL;DR
There is a bug in Mavericks that will not let you have the Special Character Viewer if you don't have your Keyboard Input Menu icon visible in the menu bar. See pictures above.​

Click to expand...

I have your exact problem, always with SystemPreferences
but with Security and Privacy Require Password after sleep or screen saver begin
I did the same thing you did, create a new user and at the beginning it worked
then after few times it became corrupted too.
I can check and uncheck the radio button and it will prompt for a password if I put the computer to sleep. If I uncheck the button it will not change the pref
and it will keep asking for a password till I don't restart with a different pref.
Leaving the preferences folder open I can see the creation of the two plist files , then one disappears
I tried to delete the one that remains but nothing to do
com.apple.screensaver.plist deleted and then a new one reappear and back to the bug
Since 3 days I'm working with this bug and another one
I have when I assign an app to open in a different desktop in spaces. Same routines with the prefs
In this case it works till I don't restart then I'm back to square one

I have your exact problem, always with SystemPreferences
but with Security and Privacy Require Password after sleep or screen saver begin
I did the same thing you did, create a new user and at the beginning it worked
then after few times it became corrupted too.
I can check and uncheck the radio button and it will prompt for a password if I put the computer to sleep. If I uncheck the button it will not change the pref
and it will keep asking for a password till I don't restart with a different pref.
Leaving the preferences folder open I can see the creation of the two plist files , then one disappears
I tried to delete the one that remains but nothing to do
com.apple.screensaver.plist deleted and then a new one reappear and back to the bug
Since 3 days I'm working with this bug and another one
I have when I assign an app to open in a different desktop in spaces. Same routines with the prefs
In this case it works till I don't restart then I'm back to square one

I found the bug! and it is a bug
I was using two different passwords for my keychain and login
If I use the same password for both I don't have any problem with locking or unlocking the screensaver.
I was able to replicate it on a brand new computer without anything installed yet, just Mavericks from Apple. Easy when you find what it is.. after one week of trying everything possible....

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